rec.autos.simulators

In a spec sheet I found the following formula to calculate a
suspension's natural frequency:

freq=3.13*sqrt(wheelRate/(frontSprungWeight/2))

'wheelRate' is in lbs/in I guess, and the frontSprungWeight is in lbs
(so the /2 is used to get the weight at one side (left or right)).

But the factor 3.13 in unclear to me. Would this be a failed attempt
to get PI in, or does anybody recognize a familiar factor to go to
Hertz for example?

Seems to me you don't need the 3.13, but it's in there and the result
looks ok (2.57 for the front suspension of a '67 Eagle F1 car)

Thanks,

Ruud van Gaal
Free car sim  : http://www.racesimcentral.net/
Pencil art    : http://www.racesimcentral.net/

The form of the resonance (or natural) frequency equation for a spring-mass
system that I've learned is

f = 1/(2*pi)*sqrt(spring constant / mass).

To get the sprung mass, you naturally have to divide the sprung weight by
the acceleration of gravity(~386 in/sec^2). Take the 386 out of the sqrt,
multiply 1/(2*pi) by it and you get 3.13 or thereabouts. :-)

Petri Blomqvist

... and, incidentally, if you're using SI units, the formula becomes

freq = 0.5*sqrt(wheelRate/(frontSprungWeight/2)),

because the square root of 9.81 m/s^2 just happens to be very close to the
value of pi... which just happens to be very close to 3.13... hmmmm.
Coincidence or design? :-)

Petri Blomqvist

  Pure coincidence I think.  The meter's length was sort of arbitrarily made up
originally.  I think it was eventually revised to be some portion of the
distance from the north pole to the equator once science entered more modern
times.  Still, it could easily have been chosen to be .1 meters longer or
shorter, it's not really a significant natural length or anything.  I use
feet/sec^2, so my 1g acceleration is 32.16 feet/sec^2, not too close to Pi :0)

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

I know it's coincidental, I was just amused by the number of numerical
coincidences here. :-)

I believe that's actually the original definition from the late 18th
century. Now it's defined (if I remember correctly) in terms of the speed of
light and the frequency of the radiation emitted by a Cesium-133 atom as it
shifts energy states, which is a bit more accurate. :-)

But note that the fractional part of your 1g acceleration is half the
integral part - coincidence or design? ;-)

Petri Blomqvist

It's too late at night for me to work it out, but
it sounds very much like a factor to get to a consistent
unit set (since lbs and ins are not renowned for this ;-)

Units appear to be sqrt(in), whatever they are!

Jonny

Getting confused by damn American units ;-)
- maybe we should all start using slugs!

Jonny

It was the height of the ancient Roman parking meter, hence the name.

<Haqsau runs away real fast>

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Well, accurate for the labs perhaps, but generally when I'm buying a
couch I don't shine a flashlight along the far side and time how long
it takes to reach the other side of the couch, and compare that with
the timing I got from my home (to see whether it fits). ;-)
In that case, having your own body is more helpful by somewhat
dividing your own length by 2 and adding some to get to 1 meter.

And 2^n, more coincidence! 2^5.2^4.
I find it nice that you only have to remember 1G by 3! => 3*2*1=6. ;-)
That saves you 2 bytes in your memory, hehe.

Ruud van Gaal
Free car sim  : http://www.marketgraph.nl/gallery/racer/
Pencil art    : http://www.marketgraph.nl/gallery/

Ruud van Gaal
Free car sim  : http://www.marketgraph.nl/gallery/racer/
Pencil art    : http://www.marketgraph.nl/gallery/

Ruud van Gaal
Free car sim  : http://www.marketgraph.nl/gallery/racer/
Pencil art    : http://www.marketgraph.nl/gallery/

Hmmm.... in that case, I wonder what would be the value of
American Pie--- I mean, Pi? :-)

Well, only if you want to use weight instead of mass in the formula.
Strangely enough, I just attended a lecture on acoustics yesterday, where I
saw the resonance frequency formula for the first time since taking basic
physics. Once again... coincidence or design? (I know, this is getting tired
:-)

By the way, note that the frequency formula we discussed only holds for
undamped oscillation. A damped system will have a lower natural frequency:

freqdamped = freq*sqrt(1-epsilon^2),

where epsilon is the damping ratio. Here's a nice web page about this stuff:
http://xenia.media.mit.edu/~verp/projects/smartpen/node17.html
(beware though, the formulae use angular frequency but the text speaks of
frequency)

But you probably knew all this already. :-)

Am I really the only one who does that? :-)

Petri Blomqvist

  Ah yes, of course :0)  I knew you knew that.... yeah.... uh huh.... sure....
:-P

  Cool.  I tried to do that once, but it's so dang hard to get those little
atoms to sit still on the table long enough to count the orbital frequency of
the electrons... ;-)

 >>  Still, it could easily have been chosen to be .1 meters longer or

  I'll be darned!  Hmmm....  More mysteries are unfolding all the time...  Must
be design :0)

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

  lol  I knew it was something like that.  I bet parking was real cheap back
then with inflation and all :0)  

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com